Impedance is a characteristic of a speaker you need to take note of, especially if connecting more than one speaker to an individual amp. See the article on Understanding Speaker Impedance for details.
The first important point to note is you should not connect a speaker combination with a total impedance lower than the minimum the amp is designed for.
For example, if your amp says the speakers should be 4-16 ohms, then connecting a 4 ohm, or 6 ohm or a 8 ohm speaker is fine. But connecting two 4 ohm speakers in parallel (which results in 2 ohms total load impedance) is too low. To calculate the total impedance of speakers in parallel see the popular Speaker in Parallel Calculator.
If you do connect a total load impedance which is lower than the amp’s minimum, you run the risk of overloading the amp; causing it to turn off, blow a fuse or blow the electronics. You can get away with a lower impedance at low volume levels, but as the amp gets close to its full output, it will get hot and stop working.
The second important point to note is you normally can have a total load impedance above the recommended maximum (Eg above 16 ohms). However the higher the load impedance, the less power the amp will be able to produce. See the article on Speaker Impedance Changes Amplifier Power.
Some amplifiers will detect that the impedance is too high and turn off thinking there is no speaker connected, but most amps will have no problem.
The exception is a tube (valve) amp. Most tube amps require some load and don’t like having no load.